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  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# vim: set filetype=python:"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Bayesian GMM with Automatic Model Selection"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In this notebook we demonstrate use of Variational Bayesian GMM with automatic model selection. Model that we use is not fully Bayesian, mixing probabilities are considered to be parameters not random variables, so we use VBEM to fit the model. VBEM algorithm consists of two steps: E step and M step.\n",
      "\n",
      "   E step : approximate posterior of all random variables (including latent variable) using Variational Bayes and evaluate lower bound. \n",
      "   \n",
      "   M step : maximize lower bound with respect to mixing probabilities.\n",
      "           \n",
      "In the process of iterations some weights are driven to zero and are pruned if they achieve threshold level (by default 1e-5). So this algorithm uses the same Automatic Relevance Determination technique that was used by Tipping in first version of RVM.\n",
      "It is also worth noting that in original paper authors used only one iteration of Variational Bayes in E step in order to speed up algorithm. There is obvious trade off between accuracy of approximation (this requires more iterations of VB in E step) and speed and sometimes it might be better to allow more iterations to improve perfomance \n",
      "(to change number of VB iterations use n_mfa_iter parameter in our implementation)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "import matplotlib.pyplot as plt\n",
      "from skbayes.mixture_models import VBGMMARD\n",
      "from matplotlib.patches import Ellipse\n",
      "import pandas as pd\n",
      "%matplotlib inline\n",
      "\n",
      "\n",
      "\n",
      "def plotter(X, max_k,title, rand_state = 1, prune_thresh = 1e-5, mfa_max_iter = 10):\n",
      "    '''\n",
      "    Plotting function for VBGMMARD clustering\n",
      "    \n",
      "    Parameters:\n",
      "    -----------\n",
      "    X: numpy array of size [n_samples, n_features]\n",
      "       Data matrix\n",
      "       \n",
      "    max_k: int\n",
      "       Maximum number of components\n",
      "       \n",
      "    title: str\n",
      "       Title of the plot\n",
      "       \n",
      "    Returns:\n",
      "    --------\n",
      "    :instance of VBGMMARD class \n",
      "    '''\n",
      "    # fit model & get parameters\n",
      "    gmm = VBGMMARD(n_components = max_k, prune_thresh = prune_thresh,\n",
      "                   n_mfa_iter = mfa_max_iter)\n",
      "    gmm.fit(X)\n",
      "    centers = gmm.means_\n",
      "    covars  = gmm.covars_\n",
      "    k_selected = centers.shape[0]\n",
      "    \n",
      "    # plot data\n",
      "    fig, ax = plt.subplots(figsize = (10,6))\n",
      "    ax.plot(X[:,0],X[:,1],'bo', label = 'data')\n",
      "    ax.plot(centers[:,0],centers[:,1],'rD', markersize = 8, label = 'means')\n",
      "    for i in range(k_selected):\n",
      "        plot_cov_ellipse(pos = centers[i,:], cov = covars[i], ax = ax)\n",
      "    \n",
      "    plt.xlabel('x1')\n",
      "    plt.ylabel('x2')\n",
      "    plt.legend(loc = 2)\n",
      "    plt.title((title + ', {0} initial clusters, {1} selected clusters').format(max_k,k_selected))\n",
      "    plt.show()\n",
      "    return gmm\n",
      "    \n",
      "    \n",
      "# plot_cov_ellipse function is taken from  \n",
      "# https://github.com/joferkington/oost_paper_code/blob/master/error_ellipse.py\n",
      "\n",
      "def plot_cov_ellipse(cov, pos, nstd=2, ax=None, **kwargs):\n",
      "    \"\"\"\n",
      "    Plots an `nstd` sigma error ellipse based on the specified covariance\n",
      "    matrix (`cov`). Additional keyword arguments are passed on to the \n",
      "    ellipse patch artist.\n",
      "\n",
      "    Parameters\n",
      "    ----------\n",
      "        cov : The 2x2 covariance matrix to base the ellipse on\n",
      "        pos : The location of the center of the ellipse. Expects a 2-element\n",
      "            sequence of [x0, y0].\n",
      "        nstd : The radius of the ellipse in numbers of standard deviations.\n",
      "            Defaults to 2 standard deviations.\n",
      "        ax : The axis that the ellipse will be plotted on. Defaults to the \n",
      "            current axis.\n",
      "        Additional keyword arguments are pass on to the ellipse patch.\n",
      "\n",
      "    Returns\n",
      "    -------\n",
      "        A matplotlib ellipse artist\n",
      "    \"\"\"\n",
      "    def eigsorted(cov):\n",
      "        vals, vecs = np.linalg.eigh(cov)\n",
      "        order = vals.argsort()[::-1]\n",
      "        return vals[order], vecs[:,order]\n",
      "\n",
      "    if ax is None:\n",
      "        ax = plt.gca()\n",
      "\n",
      "    vals, vecs = eigsorted(cov)\n",
      "    theta = np.degrees(np.arctan2(*vecs[:,0][::-1]))\n",
      "\n",
      "    # Width and height are \"full\" widths, not radius\n",
      "    width, height = 2 * nstd * np.sqrt(vals)\n",
      "    ellip = Ellipse(xy=pos, width=width, height=height, angle=theta, fill = False,\n",
      "                    edgecolor = 'k',linewidth = 4,**kwargs)\n",
      "\n",
      "    ax.add_artist(ellip)\n",
      "    return ellip\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {
      "collapsed": false
     },
     "source": [
      "Old Faithful Geyser data"
     ]
    },
    {
     "cell_type": "raw",
     "metadata": {},
     "source": [
      "Depending on tuning parameters model finds two likely cases shown below. It is worth noting\n",
      "that VBGMMARD eliminated most of irrelevant clusters leaving only 2,3 out of 20 initially defined by user."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# before running this script make sure you downloaded\n",
      "# old faithful geyser data and put it in the same directory\n",
      "# as this ipython notebook ():\n",
      "# https://github.com/AmazaspShumik/sklearn-bayes/blob/master/ipython_notebooks_tutorials/mixture_models/faithful.csv\n",
      "\n",
      "Data = pd.read_csv(\"faithful.csv\")\n",
      "Data = np.array(Data[['eruptions','waiting']])\n",
      "geyser_model_gmm1  = plotter(Data, 20,'Old Faithful')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
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998yfP58PP/zQqT3HQkJC6NKlC/369aNHjx60bdvWo877Z88a/6QVFVV2YrdX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\n+X/bnIgtm67CkwAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x105b87dd0>"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "geyser_model_gmm2  = plotter(Data, 20,'Old Faithful', mfa_max_iter = 1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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TaA8MB563/PupUVtb40wQBEHwD8ePH+fDDz9kyZIlZGVlUV5eXm2bZs2aVRhj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\nROREmJwREREROREmZ0RERERO5P8B2aO61PVuy1UAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x105b87d10>"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Clustering: Synthetic Data Example 1"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Figure below shows that VBGMMARD algorithm can get stuck in local optimum (remember optimization problem is nonconvex). However you can see that found clusters are not completely unreasonable."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "X = np.zeros([600,2])\n",
      "np.random.seed(0)\n",
      "X[0:200,:]   = np.random.multivariate_normal(mean = (0,10), cov = [[3,0],[0,2]], size = 200)\n",
      "X[200:400,:] = np.random.multivariate_normal(mean = (0,0) , cov = [[3,0],[0,2]], size = 200)\n",
      "X[400:600,:] = np.random.multivariate_normal(mean = (0,-10) , cov = [[3,0],[0,2]], size = 200)\n",
      "\n",
      "sy_gmm_1 = plotter(X,20,'Synthetic Example')\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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aUaVFGka6du1KH3/8sen3PffcQ9OnTzf9XrFiBY0ePZpeffVVmjhxosWxaWlp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\nboP//IOqwLSA0+MEY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qgEZ6XQsog8BeC0qv4lpo1LHuzGiRMR6QLgrwAedWbMKEpE5CYA\nh1R1s4hcGe/2JIk0AEMB/ERVPxKR5wH8G4BnzFa2LVW91uw+EXkQwDvO9T5yDjzvrqpHY9bABGT2\nmovIIDgi/hoRARzdaBtF5FJVPRTDJiacQO9zABCRu+Dobrg6Jg1KTl8BKPH4uwSObBlFkYikA1gA\n4A1VfTfe7UkC3wXwfRG5EUAWgK4i8rqqTopzuxLZfjh6mD5y/v1XOIIyQ525+/JdAKMBQEQuBJDB\ngCx6VHW7qp6rqv1VtT8cb7ShDMiiS0Suh6OrYZyqtsS7PQnsYwAXiEg/EckAMAHA3+LcpoQmjrO7\nPwLYqarPx7s9yUBVn1TVEud3+O0AVjAgiy5VrQewzxmnAMA1AHaYrW/rTFkQrwJ4VUS2ATgNgG+s\n2GJ3T2z8DkAGgOXODOU6VZ0S3yYlHlU9KyI/AbAUQCqAP6qq6RVSFBHfAzARwFZnwXAAmKaqS+LY\npmTD7/HYeBjAn50nfLUAfmy2IovHEhEREdlAZ+6+JCIiIkoYDMqIiIiIbIBBGREREZENMCgjIiIi\nsgEGZUREREQ2wKCMiIiIyAYYlBEReRCRJSJyTET+Hu+2EFFyYVBGROTtOQA/incjiCj5MCgjoqQk\nIiNEpEZEMkUkV0S2i8h3VHUFAE6MTUQx15mnWSIiCpuqfiQifwMwG0A2gP9W1Z1xbhYRJTEGZUSU\nzH4Bx2TkzXDMT0dEFDfsviSiZFYIIBdAFziyZS6cFJiIYo5BGREls/8E8DSAvwCY43G7xKc5RJTM\n2H1JRElJRCYBOKWqb4pICoD/E5GrAPw7gHIAXURkH4C7VXV5PNtKRMlBVJmlJyIiIoo3dl8SERER\n2QCDMiIiIiIbYFBGREREZAMMyoiIiIhsgEEZERERkQ0wKCMiIiKyAQZlRERERDbAoIyIiIjIBv4f\n1W0zbju21hAAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x109bd6150>"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Clustering: Synthetic Data Example 2 "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In this case algorithm correctly identified 3 out of 20 clusters (note all gaussian components have  the same mean with coordinates (0,0) but different covariance matrices)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "X = np.zeros([600,2])\n",
      "np.random.seed(0)\n",
      "X[0:200,:]   = np.random.multivariate_normal(mean = (0,0), cov = [[3,-2],[5,-8]], size = 200)\n",
      "X[200:400,:] = np.random.multivariate_normal(mean = (0,0), cov = [[-10,10],[-10,10]], size = 200)\n",
      "X[400:600,:] = np.random.multivariate_normal(mean = (0,0), cov = [[5,-1],[-5,-1]], size = 200)\n",
      "\n",
      "sy_gmm_2 = plotter(X,20,'Synthetic Example', prune_thresh = 1e-5, mfa_max_iter = 10)"
     ],
     "language": "python",
     "metadata": {
      "scrolled": false
     },
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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3fsdHH33E1atXLc9TqlQp3nrrLV544QVZNkoIIcQtc9sHaKLg2rt3L61bt2b/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       "text": [
        "<matplotlib.figure.Figure at 0x108e7a510>"
       ]
      }
     ],
     "prompt_number": 7
    }
   ],
   "metadata": {}
  }
 ]
}